Joint multi-Gaussian mixture model and its application to multi-model multi-bernoulli filter

Abstract

The existing multi-model Gaussian mixture-multi-Bernoulli (MM-GM-MB) filter lacks the ability to maintain parallel state estimates under different models. As a result, the change of model-related likelihoods lags behind target maneuvers. To address this problem, a joint multi-Gaussian mixture MB (JMGM-MB) filter is proposed. We first propose a JMGM model. Each single-target state estimate is expressed as a set of parallel model-related Gaussian functions with model probabilities, and a weight characterizes the probability of this state estimate. Based on the Bayesian rule, we derive the updating methods of the weights, model probabilities and model-related means, covariances that are collectively called JMGM components. Then, we approximate the state densities of MB filter using the JMGM model. Based on the interactive multi-model (IMM) method, we derive the interacting, prediction and estimation methods of JMGM components. Then, we provide matched association and merging methods for JMGM components. In nonlinear tracking scenarios where sensors simultaneously carry out translations and rotations, we derive a method based on the derivative rule for composite functions to compute the linearized observation matrix. Simulations demonstrate that whether in active or passive tracking, the proposed JMGM-MB filter overcomes the likelihood lag problem and owns higher accuracy of uncertain maneuvering target tracking than the existing MM-GM-MB filter, requiring lower computational expense.